Generating the feature image

Before generating the feature image, a non-linearity is introduced into each filtered image [20] $r_k(a,b)$, where k is the output of the $k^{th}$ filter, by applying the following transformation:

$$\phi(t) = tanh(\alpha t) = \frac{1 - e^{-2 \alpha t}}{1+ e^{2 \alpha t}}$$ (16)

For $\alpha$ = 0.25, this function acts almost as a thresholding transformation. The feature image can now be defined as:

$$e_k(x, y) = \frac{1}{M^2}\sum_{(a,b) \epsilon W_{xy}}^{}\vert\phi(r_k(a,b))\vert,$$ (17)

where $W_{xy}$ is a window of size M x M centered at pixel (x,y) in the filtered image.